Research ArticleMATERIALS SCIENCE

Energy renormalization for coarse-graining polymers having different segmental structures

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Science Advances  19 Apr 2019:
Vol. 5, no. 4, eaav4683
DOI: 10.1126/sciadv.aav4683
  • Fig. 1 Mapping from AA model to CG model of PC.

    (A) PC chemical structure and the corresponding CG bead types and their force center locations. Each monomer consists of four CG beads with three bead types. The CG bead type “A,” “B,” and “C” represent the phenylene, isopropylidene, and carbonate groups, respectively. (B) The mapping from the AA model to the CG model of a PC chain. (C) Snapshot of the simulated CG model system.

  • Fig. 2 Influence of cohesive interaction strength on dynamics of CG model.

    The Debye-Waller factor 〈u2〉 versus temperature T for the AA and CG models of PC with varying ER factor α for cohesive interaction strength. The vertical arrow indicates a dataset with increase in α. Inset: The result of α(T) for the CG model determined by preserving the T-dependent 〈u2〉 of the AA model of PC.

  • Fig. 3 Comparison of dynamics of AA and CG models over a wide range of temperature.

    (A) The MSD 〈r2〉 of the center of mass of the monomer versus time for the AA (lines) and CG (symbols) models over a wide T range. The vertical dashed line marks the time scale (around the “caging” time of 4 ps) when 〈u2〉 is obtained from the 〈r2〉 measurement. (B) T-dependent segmental relaxation time τ for the AA and CG models. As a comparison, the τ estimates from the CG models with constant ER (i.e., α = αA) and derived from the IBM exhibit a growing divergence as lowering T, while the τ estimates from the ER describe the AA τ to a much better approximation. The solid curves show the VFT fits of the τ data. The dashed curve for the CG model from the IBM shows a high T regime where the onset of sample evaporation leads to an increase in τ. Inset shows the activation energies of relaxation ΔG normalized by its value Δμ at high-T Arrhenius regime for the AA and CG models. (C) Self-diffusion coefficient D of chains at elevated T for the AA and CG models, which is well described by an Arrhenius relation (dashed line).

  • Fig. 4 Energy renormalization for CG polymers having different segmental structures.

    (A) Schematic of the developed CG models of PC, PS, and PB (from left to right) having distinct segmental structures by the ER method. The CG models are overlaid with the underlying AA models. (B) The ER factor α (normalized by its high-T limit αA) as a function of temperature for the developed CG models of PC, PS, and PB for achieving temperature-transferable coarse-graining of their dynamics.

  • Fig. 5 Analytic calculations of ER factors based on the generalized entropy theory (GET).

    (A) Temperature dependence of structural relaxation time τ for different cohesive interaction parameter ε, as calculated from the GET for a polymer melt composed of fully flexible linear chains with M = 6 and Vcell = 4 × 2.53 at a constant pressure of P = 0.101 MPa (see main text for details). The dashed line displays the result for M = 24, Vcell = 2.53, and ε/kB = 200 K, which is the analog of the AA model in the GET calculation. (B) Temperature-dependent cohesive interaction parameter ε for various M determined by applying the ER method to the GET result. The rescaling of ε is obtained by requiring an identical τ between the reference or AA (M = 24) and “CG” (lower M) models at each T. As in the case of our MD simulations, coarse-graining in the GET leads to an effective ε having a sigmoidal T dependence.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaav4683/DC1

    Section S1. Overview of MD simulations

    Section S2. Bonded potentials for the CG-PC model

    Section S3. Analytic calculations of ER based on the GET

    Fig. S1. CG bond potentials.

    Fig. S2. CG angle potentials.

    Fig. S3. CG dihedral potentials.

    Fig. S4. Density and isothermal compressibility of AA and CG models.

    Table S1. Functional forms of force field and bonded potential parameters for CG model.

    Table S2. Functional forms and parameters of the ER function for the CG model.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Overview of MD simulations
    • Section S2. Bonded potentials for the CG-PC model
    • Section S3. Analytic calculations of ER based on the GET
    • Fig. S1. CG bond potentials.
    • Fig. S2. CG angle potentials.
    • Fig. S3. CG dihedral potentials.
    • Fig. S4. Density and isothermal compressibility of AA and CG models.
    • Table S1. Functional forms of force field and bonded potential parameters for CG model.
    • Table S2. Functional forms and parameters of the ER function for the CG model.

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